Gamma Distribution in Excel

Function Details

=GAMMA.DIST (x, alpha, beta, cumulative)

Arguments of Function

• X (Required)– The value at which gamma function would be evaluated
• Alpha / α (Required) – A parameter of the distribution used for determining the shape.
• beta / β (Required) – A parameter of the distribution for determining the rate

α and β are both must be greater than 1.

When α = 1, it corresponds to exponential distribution.

When β = 1, it corresponds to the standard gamma distribution.

Cumulative (Required) – A logical value that determines the form of the function.

Cumulative =TRUE, it returns the cumulative distribution function

Cumulative =FALSE, it returns the probability density function.

Stepwise Execution

Go to an empty cell and type =GAMMA.DIST

1. Type the value where we need to find probability. This gives us the value of x. In the example below, x= 5
2. Type the alpha and beta value as the next parameters, both comma separated. Here, α = 4 & β = 3
3. Type True for cumulative distribution. Type False for probability density function.

Formula & Result

=GAMMA.DIST(5, 4, 3, TRUE)

Result: 0.088267

=GAMMA.DIST(5, 4, 3, False)

Result: 0.048579

Graph Generation Cumulative Distribution function (CDF) and Probability Density Function (PDF)

Take time T = 0 – n. In the example, time is taken from 0 to 20. Here value of T = value of x

Fix values for α = 4 & β = 3

Cumulative Distribution function (CDF)

Formula: =GAMMA.DIST(D16, 4, 3, TRUE)

Probability Density function (PDF)

Formula: =GAMMA.DIST(D16, 4, 3, FALSE)

Errors

• #NUM! – Occurs under following scenarios:

Value of x < 0

Value of α ≤ 0 or β ≤ 0

• #VALUE! – Occurs under following scenarios:

Any of the arguments – x, alpha, beta are non-numeric in nature

The fourth parameter is not TRUE OR FALSE, unrecognized